1. Heuristics of problem solving
WEEK 1
JUNE 2011

2. Topics to be discussed…
What is a problem?
What is the heuristics for problem solving?
What is the problem statement?
What is problem solving?

3. Let us look
at a problem

4. Margaret and Ian rear cats and birds
Margaret and Ian rear cats and birds. They counted all the heads and got 10. They counted all the feet and got 34. How many birds and cats do they have ?

5. Is this a problem ?
Why ?

6. SO WHAT IS A PROBLEM?
A statement or daily life situation that requires a solution.
A problem exists when a solution is not immediately obvious.

7. What is a problem ?  A situation  Blockage GOAL INITIAL STATE STATE
solution
wanted
Blockage

8. Routine
Problems
Non–Routine
Problems
2 types of Problems

9. ROUTINE PROBLEMS Text-book problems. Application of basic skills.
Involve simple mathematical operations.
Has obvious sequence of steps.
Need understanding, retrieve information given, choose the operation and apply algorithm.

10. NON-ROUTINE PROBLEMS Complex problems.
Require more then one mathematical operation.
Need understanding and synthesis, retrieve & organise given information, identify strategies and apply selected one.
Various strategies / methods.
Using critical and creative thinking skills.

11. How did you solve the problem ?

12. What are the heuristics
you use
to solve this problem ?

13. Heuristic ?
A method, “rules of thumb”, educated guesses, intuitive judgments or simply common sense

14. Some Problem Solving Heuristics

15. Popular Heuristics George Polya’s Model Krulik & Rudnick’s Model
Understand the problem
Devise a plan
Carry out the plan
Look Back
Krulik & Rudnick’s Model
Read the problem
Explore
Select a Strategy
Solve
Look BacK

16. Phase 1 :- Understanding the Problem
A clear understanding of the question and the unknown is essential for deciding what information is needed (information processing)
To consider which solution strategies and what answers are reasonable ?

17. Understanding the problem :
State the problem in your own words
Decide what the unknown is
Decide what information is needed

18. The Meaning of the Problem Statement
The ability to understand the crux of the problem;
What/which information is available/not available or relevant/irrelevant?
What is task involved embedded in the problem
An ability to restate the problem in your own words
Ensures a more successful transition
to the next phase

19. Phase 2 : Devise a Plan
Analyze various alternative solution strategies
Choose the most appropriate plan
Novice problem solvers might use a relatively inefficient trial & error approach until something works.

20. Phase 3 : - Carry Out the Plan
Carrying out the plan devised in Phase 2
Careful monitoring the solution process to check whether the plan is executed accurately & whether it is effective?

21. Decide if a new point of view is needed
Determine whether all the relevant information has been used
Consider whether there are easier ways to solve the problem

22. Phase 4 : Look Back Once a solution is obtained, check the results …
Does the solution makes sense?
Is it reasonable?
Does it answer the original question?
Decide if there are other solutions
Is there any other way the problem could be solved? Can produce the same answer? Is there a better way?

23. Now try solving
this problem

24. Sluggish Progress
A slug fell into a ditch 18 inches deep. Each day the slug moved 6 inches up the wall of the ditch, only to slip back 3 inches at night. How many days will it take the sluggish slug to reach the top of the ditch wall?

25. Think about
your thinking . . .

26. What thinking processes did you go through ?
Understand what is the problem?
Process the information related in the problem? What is important/needed?
So What now? What are my alternatives?
Strategizing?
Decision making?
Implement your decision
Review/Reflect…is there a better way?

27. What then is
problem solving ?

28. PROBLEM SOLVING
Is a systematic process that uses one’s knowledge, experience, thinking skills and various strategies in order to solve and make decision.
According to National Council Teachers of Mathematics
(NCTM ) Standards, Problem Solving is the process
by which students experience the power and usefulness
of mathematics in the world around. It is also a
method of inquiry and application to provide a
consistent context for learning and applying maths
Problem situations can establish a 'need to know
and foster the motivation for the development of
concepts.
Satu proses terancang yang memerlukan pengetahuan,
pengalaman yang telah diperoleh, kemahiran berfikir
dan pelbagai strategi untuk mencapai matlamat yang
dikehendaki dalam sesuatu masalah.

29. Why problem solving ?

30. Preparing one for daily life’s problem solving skills
Understanding the problem
Processing the information
Finding alternatives/strategies
Decision making
Review …
Accept responsibility. Learning from mistakes. Perseverance. Confidence.

31. Tutorial
In small groups, devise a problem-solving activity for primary school children.
Then, think of possible difficulties faced by primary school children when solving the problem, and identify possible non –mechanical method to solve the problem
Group presentation